Suppose you are standing at the earth's geographic north magnetic pole, the place on the earth's surface that compasses point to
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A) Vector A
The x-component of a vector can be found by using the formula
where
v is the magnitude of the vector
is the angle between the x-axis and the direction of the vector
- Vector A has a magnitude of 50 units along the positive x-direction, so . So its x-component is
- Vector B has a magnitude of 120 units and the direction is (negative since it is below the x-axis), so the x-component is
So, vector A has the greater x component.
B) Vector B
Instead, the y-component of a vector can be found by using the formula
Here we have
- Vector B has a magnitude of 50 units along the positive x-direction, so . So its y-component is
- Vector B has a magnitude of 120 units and the direction is , so the y-component is
where the negative sign means the direction is along negative y:
So, vector B has the greater y component.